I came across this limit when I was trying to derive the derivative of the factorial function: \(\dfrac{d(n!)}{dn} = n!(H_n - \gamma)\) for all whole numbers \(n\). Let's denote the derivative as \(D(n)\) We know that \((n+1)! = (n+1)n!\). Therefore, differentiating gives us:

Hey Ariel, I see that you like to solve difficult calculus questions. We got a group on another social platform (online forum) that discusses all kinds of difficult calculus questions as well. Plus, most of the active members on Brilliant are on this online forum as well (even the staffs!). We discuss about everything related to math and science. Plus, it's free! Would you like to join us?